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The Fate of the Universe Evolution in the Quadratic Form of Ricci–Gauss–Bonnet Cosmology

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Abstract

We investigate the possibility of a future singularity due to accelerating expansion of the Universe in a gravitational theory that comprises the Ricci scalar \(R\) and the Gauss–Bonnet invariant \(\mathcal{G}\), known as \(F(R,\mathcal{G})\) gravity, which can be viewed in the quadratic form. Three models are presented using Hubble parameters to represent a finite and infinite future. The model parameters are analyzed on the basis of their physical and geometrical properties. This study also explores the properties of the modified gravitational theory, and neither a future singularity nor a little or pseudo-rip are posed as threats to the fate of the Universe. We present scalar perturbation approaches to perturbed evolution equations and demonstrate their stability.

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References

  1. A. G. Riess et al., Astron. J. 116, 1009 (1998).

    Article  ADS  Google Scholar 

  2. S. Perlmutter et al., Astrophys. J. 517, 565 (1999).

    Article  ADS  Google Scholar 

  3. P. A. R. Ade (Planck Collaboration) et al., Astron. Astrophys. A13, 594 (2016).

    Google Scholar 

  4. N. Aghanim (Planck Collaboration) et al., Astron. Astrophys. 641, A6 (2020).

    Article  Google Scholar 

  5. S. Nojiri, S. D. Odintsov, and M. Sami, Phys. Rev. D. 74, 046004 (2006).

    Article  ADS  Google Scholar 

  6. S. Nojiri and S. D. Odintsov, J. Phys. Conf. Ser. 66, 012005 (2007).

    Article  Google Scholar 

  7. S. V. Lohakare, K. Rathore, and B Mishra, arXiv: 2303.14575.

  8. E. Elizalde et al., Class. Quantum Grav. 27, 095007 (2010).

    Article  ADS  Google Scholar 

  9. A. de la Cruz-Dombriz and D. Saez-Gomez, Class. Quantum Grav. 29, 245014 (2012).

    Article  ADS  Google Scholar 

  10. S. V. Lohakare et al., Phys. Dark Universe 36, 101164 (2023).

    Article  Google Scholar 

  11. V. K. Oikonomou, Astrophys. Space Sci. 361, 211 (2016).

    Article  ADS  Google Scholar 

  12. S. V. Lohakare, S. K. Tripathy, and B. Mishra, Phys. Scr. 96, 125039 (2021).

    Article  ADS  Google Scholar 

  13. K. Atazadeh and F. Darabi, Gen. Rel. Grav. 46, 1664 (2014).

    Article  ADS  Google Scholar 

  14. M. F. Shamir and A. Komal, Int. J. Geom. Meth. Mod. Phys. 14, 1750169 (2017).

    Article  Google Scholar 

  15. R. Singh, New Astronomy 85, 101513 (2021).

    Article  Google Scholar 

  16. M. Z. Bhatti, Z. Yousaf, and A. Rehman, Phys. Dark Universe 29, 100561 (2020).

    Article  Google Scholar 

  17. M. F. Shamir and S. Zia, Can. J. Phys. 98, 9 (2020).

    Article  Google Scholar 

  18. M. Alimohammadi and A. Ghalee, Phys. Rev. D. 79, 063006 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  19. M. de Laurentis, M. Paolella, and S. Capozziello, Phys. Rev. D. 91, 083531 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  20. S. D. Odintsov, V. K. Oikonomou, and S. Banerjee, Nucl. Phys. B 938, 935 (2019).

    Article  ADS  Google Scholar 

  21. K. Bamba et al., JCAP 04, 001 (2015).

  22. B. J. Barros, E. M. Teixeira, and D. Vernieri, Ann. of Phys. 419, 168231 (2020).

    Article  Google Scholar 

  23. I. de Martino, M. de Laurentis, and S. Capozziello, Phys. Rev. D 102, 063508 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  24. S. Nojiri et al., Nucl. Phys. B. 973, 115617 (2021).

    Article  Google Scholar 

  25. R. R. Caldwell, M. Kamionkowski, and N. N. Weinberg, Phys. Rev. Lett. 91, 071301 (2003).

    Article  ADS  Google Scholar 

  26. E. Babichev, V. Dokuchaev, and Yu. Eroshenko, Phys. Rev. Lett. 93, 021102 (2004).

    Article  ADS  Google Scholar 

  27. E. Komatsu et al. [WMAP Collaboration], Astrophys. J. Suppl. Ser. 192, 18 (2011).

    Article  ADS  Google Scholar 

  28. A. A. Starobinsky, Grav. Cosmol. 6, 157 (2000).

    ADS  Google Scholar 

  29. L. Fernandez-Jambrina and R. Lazkoz, Phys. Rev. D 74, 064030 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  30. P. H. Frampton, K. J. Ludwick, and R. J. Scherrer, Phys. Rev. D 84, 063003 (2011).

    Article  ADS  Google Scholar 

  31. P. H. Frampton, K. J. Ludwick, and R. J. Scherrer, Phys. Rev. D 85, 083001 (2012).

    Article  ADS  Google Scholar 

  32. M. Sami and A. Toporensky, Mod. Phys. Lett. 19, 1509 (2004).

    Article  ADS  Google Scholar 

  33. I. Brevik, E. Elizalde et al., Phys. Rev. D 84, 103508 (2011).

    Article  ADS  Google Scholar 

  34. K. Bamba et al., Phys. Rev. D 85, 104036 (2012).

    Article  ADS  Google Scholar 

  35. Diego Saez-Gomez, Class. Quantum Grav. 30, 095008 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  36. A. N. Makarenko, V. V. Obukhov, and I. V. Kirnos, Astrophys. Space Sci. 343, 481 (2013).

    Article  ADS  Google Scholar 

  37. I. Brevik, A. V. Timoshkin, and Y. Rabochaya, Mod. Phys. Lett. A 28, 1350172 (2013).

    Article  ADS  Google Scholar 

  38. B. Mishra and S. K. Tripathy, Phys. Scr., 95, 095004 (2020).

    Article  ADS  Google Scholar 

  39. P. P. Ray et al., Forts. der Physik 69, 2100086 (2021).

    Article  Google Scholar 

  40. J. B. Jimenez, L. Heisenberg, and T. Koivisto, Phys. Rev. D 98, 044048 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  41. J. B. Jiménez, L. Heisenberg, T. S. Koivisto, and S. Pekar, Phys. Rev. D 101, 103507 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  42. M. Koussour, S. H. Shekh, M. Bennai, Phys. Dark Universe 36, 101051 (2022).

    Article  Google Scholar 

  43. M. Koussour, S. H. Shekh, M. Govender, and M. Bennai, J. High Energy Astroph. 37, 15–24 (2023).

    Article  ADS  Google Scholar 

  44. L. Pati et al., Phys. Dark Universe 35, 100925 (2022).

    Article  Google Scholar 

  45. B. Li, J. D. Barrow, and D. F. Mota, Phys. Rev. D 76, 044027 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  46. G. Cognola et al., Phys. Rev. D 75, 086002 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  47. S. V. Lohakare et al., Universe 8 (12), 636 (2022).

    Article  ADS  Google Scholar 

  48. R. R. Caldwell, Phys. Lett. B 545, 23 (2002).

    Article  ADS  Google Scholar 

  49. P. Steinhardt, L. Wang, and I. Zlatev, Phys. Rev. D 59, 123504 (1999).

    Article  ADS  Google Scholar 

  50. S. Nojiri et al., Phys. Rev. D 71, 063004 (2005).

    Article  ADS  Google Scholar 

  51. D. Camarena et al., Phys. Rev. Res. 2, 013028 (2020).

    Article  Google Scholar 

  52. S. M. Feeney, D. J. Mortlock, and N. Dalmasso, Mon. Not. R. Astron. Soc. 476, 3861 (2018).

    Article  ADS  Google Scholar 

  53. R. Amanullah et al., Astroph. J. 716, 712 (2010).

    Article  ADS  Google Scholar 

  54. G. Hinshaw et al., Astrophys. J. Suppl. Ser. 208, 19 (2013).

    Article  ADS  Google Scholar 

  55. S. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, 1973).

    Book  MATH  Google Scholar 

  56. E. Poisson, A Relativist’s Toolkit: The Mathematics of Black Hole Mechanics (Cambridge University Press, 2004).

    Book  MATH  Google Scholar 

  57. S. Carroll, Addison Wesley 101, 102 (2004).

  58. A. de la Cruz-Dombriz and D. Saez-Gomez, Class. Quantum Grav. 29, 245014 (2012).

    Article  ADS  Google Scholar 

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Funding

SVL acknowledges the financial support provided by the University Grants Commission through the Junior Research Fellowship (Ref. no. 191620116597) to carry out the research work. F. Tello-Ortiz thanks the financial support of projects ANT-1956 and SEM 18-02 at the Universidad de Antofagasta, Chile. F. Tello-Ortiz acknowledges the PhD program Doctorado en FAsica mencion en Fisica Matematica de la Universidad de Antofagasta for continuous support and encouragement. BM and SKT acknowledge IUCAA, Pune, India, for support through the visiting associateship programme.

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Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, 500078, Hyderabad, India

    Santosh V Lohakare & B. Mishra

  2. Departamento de Física,Facultad de Ciencias Basicas, Universidad de Antofagasta, Antofagasta, Casilla 170, Chile

    Francisco Tello-Ortiz

  3. Department of Physics, Indira Gandhi Institute of Technology, Sarang, 759146, Dhenkanal, Odisha, India

    S. K. Tripathy

Authors
  1. Santosh V Lohakare
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  2. Francisco Tello-Ortiz
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  3. B. Mishra
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  4. S. K. Tripathy
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Corresponding authors

Correspondence to Santosh V Lohakare, Francisco Tello-Ortiz, B. Mishra or S. K. Tripathy.

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Lohakare, S.V., Tello-Ortiz, F., Mishra, B. et al. The Fate of the Universe Evolution in the Quadratic Form of Ricci–Gauss–Bonnet Cosmology. Gravit. Cosmol. 29, 443–455 (2023). https://doi.org/10.1134/S0202289323040138

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  • DOI: https://doi.org/10.1134/S0202289323040138

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